INTRODUCTORY OBSERVATIONS. 13 



tion, in the place of two which it ought otherwise to have con- 

 tained, and, which has thus enabled us to effect the simplification 

 in question, seems worthy of the attention of analysts, and may 

 be of use in other researches where equations of this nature are 

 employed. 



We will now give a brief account of what is contained in the 

 following Essay. The first seven articles are employed in de- 

 monstrating some very general relations existing between the 

 density of the electricity on surfaces and in solids, and the cor- 

 responding potential functions. These serve as a foundation to 

 the more particular applications which follow them. As it 

 would be difficult to give any idea of this part without employ- 

 ing analytical symbols, we shall content ourselves with remark- 

 ing, that it contains a number of singular equations of great 

 generality and simplicity, which seem capable of being applied 

 to many departments of the electrical theory besides those con- 

 sidered in the following pages. 



In the eighth article we have determined the general values 

 of the densities of the electricity on the inner and outer surfaces 

 of an insulated electrical jar, when, for greater generality, these 

 surfaces are supposed to be connected with separate conductors 

 charged in any way whatever; and have proved, that for the 

 same jar, they depend solely on the difference existing between 

 the two constant quantities, which express the values of the 

 potential functions within the respective conductors. After- 

 wards, from these general values the following consequences have 

 been deduced : 



When in an insulated electrical jar we consider only the 

 electricity accumulated on the two surfaces of the glass itself, 

 the total quantity on the inner surface is precisely equal to that 

 on the outer surface, and of a contrary sign, notwithstanding the 

 great accumulation of electricity on each of them: so that if 

 a communication were established between the two sides of the 

 jar, the sum of the quantities of electricity which would manifest 

 themselves on the two metallic coatings, after the discharge, is 

 exactly equal to that which, before it had taken place, would 

 have been observed to have existed on the surfaces of the coat- 

 ings farthest from the glass, the only portions then sensible to 

 the electrometer. 



